Determination of signal-to-noise ratios and spectral SNRs in cryo-EM low-dose imaging of molecules.

The single-particle images employed in this study were from two ribosomal samples: the first set was the 70S E. coli ribosome stalled in the pre-accommodation state with the antibiotic kirromycin ( Valle et al., 2003 ). This kirromycin-stalled ternary complex was previously found to have tRNA in both the E and P sites, with aa-tRNA-EF-Tu-GDP bound in over 70% of the ribosome population ( Valle et al., 2003 ). The second data set consisted of the 80S ribosome from the thermophilic fungus Thermomyces lanuginosus . Sordarin was used to trap the ADP-ribosylated factor eEF2 (ADPR-eEF2) in the GDP state, preventing the dissociation of eEF2-GDP from the 80S ribosome ( Taylor et al., 2007 ). The grids had a thin carbon support, estimated to be 15–20 nm thick. Film micrographs were obtained under low-dose conditions on a Tecnai F30 Polara electron microscope (FEI) at 300 kV, at 59,000X magnification, with the specimen at liquid nitrogen temperature (80°K). A series of four defocus levels was used in the range of 1–4 μ. For dual exposures, the dose was approximately 22 electrons/A 2 for each exposure. Kodak SO163 EM Film was developed at 20° C in full strength Kodak D19 developer, washed 1 minute in circulating water, and then fixed for 4.5 minutes in Kodak Rapid fixer. The micrographs were digitized with a step size of 7 μ (3629 dpi) on a Photoscan 2000 (Z/I Imaging Corp., Huntsville, AL), resulting in a pixel size of 1.2 Å on the object scale. The scanner output is in transmittance values, T, which are related to optical density (OD) values by the formula OD = −LogT. In the film negatives, the ribosomes have higher transmittance and thus lower optical density compared to the background, which, when scanned, result in particles lighter than the background. To make the particles darker (more positive OD) than the background, the minus sign is omitted from the above formula, and an arbitrary constant (+5) is added. For dual scans, the same micrograph film is simply left mounted on the scanner glass and digitized a second time. The program zi2spi ( www.wadsworth.org/spider_doc/spider/docs/techs/recon/mr.html ) was used to convert scanner TIFF files to SPIDER format. The remainder of the image processing was carried out with SPIDER software ( Frank et al, 1996 ). For the dual exposure measurements, the digitized micrograph pairs were aligned using a series of SPIDER procedure files that calculate the shifts and rotations for sub-regions of the micrographs, and then combine these into the total shift and rotation required to bring the micrographs into overall register. On average, micrographs had to be rotated by less than 1 degree (0.9°) to be aligned. To assess the contribution of beam-induced movement, a montage of sample particle images was created from each micrograph of the dual-exposure pairs. The display was rapidly alternated between the two arrays of images –particles changing position would appear to jump back and forth. No particles were observed to do so in the sampling from each micrograph. These results suggest that the micrograph alignments were accurate, and that particles did not move as a result of the second exposure. Thus each micrograph set consisted of a first exposure (the reference micrograph), a second exposure, and a second digitization of the first exposure. Single-particle images were windowed from the digitized reference micrographs using an automated procedure which centered and normalized each putative particle, followed by manual selection. The window diameter was 300 pixels (360 Å). 3100 particle images were obtained from 4 reference micrographs in the first data set (70S ribosome), 6300 particle images were obtained from 17 reference micrographs in the second data set (80S ribosome). The corresponding particle images were windowed from the second exposure and second digitization micrographs for the dual-exposure and dual-scan studies, respectively. To compare particle images with the same orientation, particle images from the reference micrographs were run through the single-particle alignment and reconstruction procedure. The assigned 3D Euler angles were refined to 1 degree angular ‘bins’. For the angular bins containing more than 1 assigned particle image, the images contained therein were compared pair-wise. The SNR was computed from the cross-correlation coefficient, ρ , using SPIDER’s “CC C” operation, which computes the cross correlation coefficient between two pictures over an area defined by a mask function. The mask used in this study was a disk with the same diameter as the ribosome (220 pixels or 264 Å). The values of ρ of all images from a given micrograph pair were averaged together and converted to SNR, using equation 1 . Fourier ring correlations (FRCs) were computed between pairs of images, using SPIDER’s “RF” operation. Images were masked with a “soft” Gaussian mask with full width at half maximum corresponding to the edge of the above “hard” mask (σ= 94 pixels). FRCs from all image pairs in the dual-scan, dual-exposure, and same-reference sets were averaged together to create an average FRC for each of these three conditions. These were then converted to spectral SNRs (SSNRs) using equation 4 . Points corresponding to zeroes in the CTF were excluded from the calculation of SSNR.

Creation of Phantom Dataset

Our study has shown that to be realistic, phantom image data required for the testing and validation of new approaches to classification must include a structural noise term of a size roughly matching the signal. This noise portion gives rise to an image noise component that is unrelated to the object yet CTF-dependent. In the creation of phantom data, the noise term needs to be added to the projection of the 3D model structure, and the resulting “contaminated” image then needs to be subjected to the CTF before the shot noise and any noise from subsequent sources are added. In this context, it should be noted that recently, Zeng et al. (2007) also included a CTF-dependent noise contribution in a model of EM images derived from two-dimensional crystals. A simulated dataset with structural heterogeneity was computed according to the measured SNR values reported in this work. Two density maps of the 70S E. coli ribosome complexes in different conformations were used to generate the data. These reconstructions had been previously obtained ( Scheres et al. 2007 ) using a maximum likelihood-based classification from ~90,000 cryo-EM images of a heterogeneous sample of ribosome complexes (original source: Måns Ehrenberg, Uppsala). Map #1 represents the ribosome bound with three tRNAs at the A, P, and E sites, while map #2 represents an EF-G•GDPNP-bound ribosome with a deacylated tRNA bound in the hybrid P/E position. Besides differences in the binding of the ligands, the two maps also reflect differences in the ribosomal conformations: map #1 represents the normal conformation, while map #2 represents the ratcheted conformation (i.e., with the 30S subunit rotated counter-clockwise relative to the 50S subunit). First, 5000 projection images were generated from each map with randomly distributed orientations (Eulerian angles ψ=0°; θ=0°–90°; ϕ= 0°–360°). Second, to simulate the structural noise, different realizations of random noise with zero-mean Gaussian distribution were added to all the projection images such that the resulting images had an SNR of 1.4 (see α true_struct in Table 3 , column 1). Next, these noisy images were subjected to modulation by a contrast transfer function (CTF) that simulates the effect of the FEI Tecnai F30 Polara transmission electron microscope (Cs=2.26mm) operated in the bright-field mode at 300 kV and 2 μ underfocus. Finally, another set of zero-mean Gaussian noise images were added to simulate the effects of shot noise and digitization noise, which brought the final SNR to 0.05 (see α comp_struct in Table 3 , column 1), in agreement with the SNR measurements. Fig. 5 compares a set of such simulated images (bottom row) with some of the experimental images used in this study (top row), both at 2 μ defocus.